Theory of
supernova
remnants
Rino Bandiera
INAF – Arcetri Astrophysical Obs.
FOE17 Fifty-One Erg
Corvallis, OR, June 5-8, 2017
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The many reasons to study SNRs
• Debris of a stellar explosion  footprints of the explosion itself
characteristics of the SN progenitor
• Properties of the ambient medium  density, magnetic, field, etc.
• Collisionless shocks  realm of complex microphysical processes
B-mediated interactions, plasma instabilities
unrivaled plasma laboratory
• Best candidate sources of CRs  physics of particle acceleration
CR dynamical feedback
• Wealth of observational data  from radio to TeV gamma rays
several kinds of radiation, both
thermal and nonthermal processes
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Cut of this talk
• Focus on some diagnostic tools  getting insight of the microphysics
• The diagnostic power of Balmer-line emission
• Radio and non-thermal X-rays  probing the accelerated electrons
• Electron CRs  energetically less important than hadrons
BUT
leading actor of all the detailed phenomenology
of non-thermal, and polarized, emission
• Importance of geometry, to match data and theory
• Focus on a few ‘clean’ cases (mainly SN1006)
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Collisionless shock waves
• Long collisional mean free paths
• But electrons and ions mainly interact with magnetic fields
• In a homogenous field, particles spiraling with small gyration radii
• In the presence of B field perturbations, resonant scattering
(particle-wave interaction)
• Gyration radius as the reference length scale
• For a highly chaotic field (Bohm’s limit), equal to the mean free path
Associated diffusion coefficient
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Particle acceleration
• SNRs as the main candidate sources of Galactic Cosmic Rays:
particles accelerated at the shock front
• Best candidate mechanism is Diffusive Shock Acceleration
• Particles gain energy from bouncing back and
forth through the shock (converging flows)
1st-Order Fermi Acceleration
flow speed, u1
shock
• Necessary ingredient:
‘Scattering centers’
(both upstream and downstream)
u2
Upstream
Downstream
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(Bell 1978)
• Average momentum gain per cycle
• Return probability from the downstream
• Power-law momentum distribution
• γ linked to compression factor
(strong shock: r = 4  s = 2)
• Where is the physics?
Duration of cycle  Acceleration rate
(Forman & Morfill 1979; Drury 1983)
• More efficient if  small (i.e. small mean free paths)
Efficient scattering needed also in the upstream !
Maximum energy
• While the only limit to ions acceleration is set by the SNR age, or by
the SNR size…
• Electrons energization is much sooner balanced by radiation losses
• Upper frequency cutoff independent of the magnetic field
• In the X-ray range, for SNR velocities and Bohm diffusion
FIRST ‘COSMIC’ CONSPIRANCY
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Feedback on the shock structure
In the case of efficient (ion) Cosmic-Ray acceleration
• CR streaming  gradients upstream of the shock.
Shock precursor
• CR streaming instabilities  magnetic turbulence
in the upstream.
Field amplification
• (Magnetic) scattering centers will speed up the
acceleration process. Positive feedback
• Particles at different energies see different shock
compression ratios  the particle spectrum does
no longer follow a pure power law. Concavity
• Efficient particle acceleration drains energy from
thermal motions. Lower temperature downstream
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SNR shocks as efficient CR sources
How to test?
• Accelerated hadrons:
– Production and decay of neutral pions ( gamma rays )
BUT
– Inverse Compton radiation, by the accelerated electrons
( scattering on ambient photons – also gamma rays )
• The former implies strong B (amplified by CR induced turbulence).
• The latter (for consistency with the observed X-ray synchrotron)
implies a weaker field  low CR efficiency
SECOND ‘COSMIC’ CONSPIRACY
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• The Agile team announced discovery in SNR W44 of the ‘pion
bump’, a distintive feature near 200 MeV interpreted as thr threshold
of the neutral pion decay
(Giuliani et al. 2011)
• Fermi-LAT measurements confirmed it, and found it also in the
spectrum of SNR IC443
(Ackermann et al. 2013)
BUT
• Then proved that CR production not needed!
Just reacceleration of Galactic CRs
(Cardillo et al. 2016)
RESULTS VERY UNCERTAIN AND MODEL DEPENDENT
The ‘smoking gun’ should be found somewhere else
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OTHER STRATEGIES:
• Large B field at the shock (efficient turbulent amplification)
• Shocked thermal ions are cooler (part of energy absorbed by CRs)
• Compression ratio <4 at the shock (as predicted for modified shocks)
• Direct detection of a precursor, or of its effects
Investigation using:
• Synchrotron emission, in radio and X-rays
• Balmer lines
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Radio Synchrotron:
• With power-law particle distribution
the synchrotron emission becomes
• Then:
for r = 4  s = 2  sp.index = 0.5
• Radio spectral indices of SNRs:
indeed scattered around 0.5 
• No evidence of shock modification.
But radio SNR sample is dominated
by older objects, near the end of the
adiabatic expansion phase
(Bandiera & Petruk 2010)
(Dubner & Giacani 2015)
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X-ray Synchrotron:
• Evidence of synchrotron cutoff in the X-ray range
 diffusion coefficient not much larger than Bohm limit
• Non-thermal emission confined in thin filaments:
estimated fields 100-300 G (Hwang et al. 2002, Bamba et al. 2005, Warren et al.
2005, Katsuda et al. 2010, Eriksen et al. 2011, etc.)
BUT
• Also explanation involving rapid magnetic field damping (Pohl et al. 2010)
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Another ‘cool’ diagnostic tool
‘NON-RADIATIVE’ Balmer emission
• The riddle of pure Balmer emission from some SNRs (e.g. Tycho, SN1006)
• Unusual line profile, showing a narrow and a broad component
• Excluded emission from a ‘radiatively cooling’ plasma
• Collisionless shocks in partially neutral medium
• Neutral particles unaffected during crossing
• Their further evolution is purely collisional
• Competition between collisional processes
• Collisional excitation leads to ‘still kinetically cold’
emitting hydrogen (narrow line component)
• Charge-exchange ‘neutralizes’ shocked protons.
These ‘kinetically hot neutrals’ are responsible of
the broad line emission
• Eventually all neutrals are ionized
(Chevalier & Raymond 1978) 14
(Chevalier et al. 1980)
Diagnostics from Balmer lines
• Soon recognized the diagnostic potential of this emission
• Being 𝜎𝑐ℎ−𝑒𝑥 rapidly decreasing with the relative velocity,
the 𝐼𝑏 /𝐼𝑛 ratio depends on 𝑉𝑠ℎ .
• The 𝐼𝑏 /𝐼𝑛 ratio also depends on the
level of equilibration 𝑇𝑒 /𝑇𝑖 (a.k.a. 𝛽 )
between electrons and ions
• Also the broad line width ( 𝑊 )
depends on both 𝑉𝑠ℎ and 𝛽
• Less testable the gas density and the
neutral density fraction (related to the
observed surface brightness, but one
should know the path length)
(Smith et al. 1991)
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The creation of diagnostic diagrams
• Modelling the spatial structure of Balmer-dominated shocks
• Improving the cross sections for the various processes, and follow
the whole reaction tree (for collisional excitation, charge exchange, ionization)
• Taking into account the velocity
dependence of cross sections
• Including also helium
(Some milestone:
Ghavamian et al. 2001,
Heng & McCray 2007,
Heng et al. 2007,
van Adelsberg 2008)
(Heng 2010)
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Efficiency of electron heating in shocks ?
• Thanks to a fit of Balmer lines one can test the dependence of
the temperature equilibration on 𝑉𝑠ℎ
−2
• Different authors agree on a 𝛽 ∝ 𝑀𝑠ℎ
dependence
(Ghavamian et al. 2007)
(van Adelsberg et al. 2008)
Also review by Ghavamian et al. 2013
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A kinetic approach
(the ‘Arcetri team’, especially G.Morlino)
• Neutrals do not behave like a gas. Use of Vlasov equations.
Velocity distributions deviate considerably from maxwellians.
• Each charge-exchange process (for H) ‘kills’ a neutral atom and
‘creates’ another one: series of generations (k) of neutrals
• For k=1 and more, they
can cross the shock back
(‘neutral return flux’)
• Charge-exchange in the
upstream, leading to
higher temperatures and
lower bulk velocities
(shock precursor – more
relevant for slower shock)
Blasi et al. 2012
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Effects on the line profiles
• Neutral return flux  a ‘neutral induced’ precursor
• Charge-exchange in the precursor  some Balmer in the upstream
• Upstream protons heated up to
106-107 K  charge exchange with
them leads to the formation of an
‘intermediate’ spectral component
(more apparent in the case of large
neutral fractions). (Morlino et al. 2012)
• Maybe related to previously observed ‘non-Maxwellian’ profiles?
•
(Raymond et al. 2008)
Recently shown (Ghavamian et al. 2017,
integral spectroscopy in SNR
N103B) line profiles that needs 3-component fit (the intermediate
having FWHM 125-225 km/s)
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Broadening of the ‘narrow line’ component
• Effect recognized since long ago (Smith et al. 1994), and different from
the intermediate component.
• If thermal broadening, T 
30,000 K.
Why not fully ionized?
First attempts to justified it:
• Thermal conduction precursor
• Photoionization precursor
• MHD precursor
• Broad component neutral
precursor
• Cosmic-ray precursor

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Diagnostics of efficient CR production?
(Morlino et al. 2013)
The presence of neutrals, with the formation of the neutral precursor,
tends to decrease the concavity of the accelerated particle spectrum
The presence of CRs would affect Balmer emission in two ways:
• If efficient CR production drains energy, a narrower ‘broad
component’ is expected
BUT large spread, depending also on the level of T equilibration
• The extra heating in the CR-induced precursor may broaden the
narrow component
BUT only if ions in the precursor are efficiently heated by turbulence
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Diagnostic diagram for the broad component
(Morlino et al. 2013b)
The FWHM:
• Increases with shock velocity
• Decreases with increasing CR efficiency
• Decreases with increasing T equilibration
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Possible detections of the CR precursor
• Knot g in Tycho’s SNR
(Ghavamian et al. 2000)
(Lee et al. 2010)
• Recent hint also for a filament in Cygnus Loop (Katsuda et al. 2016)
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The NW filament in SN 1006
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The analysis in Raymond et al 2007
• Balmer filament on the NW side of SN 1006
• HST high spatial resolution
(pixel size = 1.6 1015 cm @ 2.1 kpc)
• Novel approach. Assumption:
• Rippled layer almost edge-on
• Shock surface concave outwards
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Fits to filaments radial profile
• Scale length in the inner part
is determined by the physics
 mean free paths
 gas density
• Scale length in the outer part
is determined by the geometry
 local radius of curvature
 length scale along the path
 emissivity
 neutral fraction
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• Fit not very accurate
• Very small inferred curvature radii (1/100 of the filament length)
• Suggested magnetic field to lie near the plane of the sky, to
account for smaller scales along the line of sight
BUT IMPORTANT INSPIRING SUGGESTIONS
• ‘possible that the bright filament at position 28 contains more than one
tangency to the line of sight, broadening the spatial profile and increasing
the total brightness’
• ‘bulk motions contribute at most 6% to the measured line widths when
added in quadrature to the thermal widths’
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A toy model for the surface ripples
Assume:
• very thin emitting sheet
• constant face-on surface brightness
• ‘ad-hoc’ power spectrum of radial
fluctuations
(isotropic)
• then mapped on a spherical surface,
seen edge-on
Simulated map
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Selection of some bright filaments
For them, more than one
tangency seems to be the rule.
Selecting the brightest filaments
leads to this selection effect.
29
More recent data in Nikolic et al 2013
Fine grid of high resolution spectra (VIMOS @ VLT)
• Sensibly different values of W, and of Ib/In from nearby regions
• Signs of small-scale changes of physical quantities ?
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‘Work in progress’ results
Started collaboration, on this subject,
with Sladjana Knezevic (=Nikolic) and Giovanni Morlino
AIMS
• Prove that, as it seemed, the filament is spatially resolved
• Investigate which observed effects explained by pure geometry
• Refine physical model, and derive new physical parameters
• Assess the importance of geometrical effects
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First motivations
• Very similar (within 3%) Vsh between
bright filament and outer edge 
• Outer edge consistent with a finite
thickness layer (scale size  0.9 arcsec)
Fit with exponential profile
(Winkler et al 2003)
HST data courtesy
of John Raymond
• Search for scenario with spatially resolved filament
• …and with not so large physical variation over short scales
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Broadening of the broad component
• As an effect of quadratic combination with bulk motions
(if two layers intercepted)
As suggested by Raymond et al. 2007
• Required aspect angle for the two layers: about 10o
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Effects of positive or negative curvature
Toy model for the spatial profile of narrow & broad em. components
Convex
Concave
Curvature
Curvature
THIS IS NOT
A FIT
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Velocity shifts of the broad component
• A result of the fits to the line shapes
• Distribution with   100 km/s
• Unexpected, for an absolutely
homogenous layer
• Required different face-on surface brightnesses (Aa and Ab)
• Sufficient  50 % differences, over larger scales ( 0.1 pc)
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Spatial structure and geometry
• If spatial resolution allows  fit spatial behaviour of Balmer emission
BUT
• In real life little chance to observe, edge on, a plane parallel shock
• Importance of modelling not only the physics, but also the geometry
•
•
•
•
Effects on the spatial profile of the emission
Effects on the Ib/In ratio
Effects on the width of the broad component
Effects on the centroid of the broad component
CAVEAT for spatially resolved analyses of the emission
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Synchrotron polarization
• Homogeneous magnetic field  Very high polarization degree
about 70%, for s = 2
• Typical polarization degrees in SNRs: 10-15%
• Higher values up to 35-60% in some special locations
(like in Vela SNR, DA 530, G107.5-1.5, SN 1006; e.g. Dubner & Giacani 2015)
• + (internal) Faraday rotation  longitudinal B
Large scale magnetic field pattern
DA 530
(Kothes & Brown 2009)
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Field pattern of younger and older SNRs
The dichotomy between younger and older SNRs.
(Milne 1987)
‘It appears on examination of the magnetic field maps that radial fields are more
prevalent than tangential fields and that these are mainly in the young remnants.’
CTB 1
Cas A
From W. Reich
(maps of the B direction)
Swept up field
Projection effect? Why preferentially in young SNRs?
• Are radially oriented fields an effect of instabilities?
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Bilateral SNRs
SN 1006
(Kesteven & Caswell 1987, Roger et al. 1988)
… plus several other, although less evident, cases.
• Soon recognized as a tool to investigate obliquity dependence of
(electron) shock acceleration.
(Fulbright & Reynolds 1990)
• Statistical analyses to test relations with Galactic magnetic field
(Bisnovatyi-Kogan et al. 1990, Gaensler 1998, West et al. 2016, 2017)
• Quasi-perpendicular acceleration  Barrel-like 3-D emission
• Quasi-parallel acceleration  Polar-caps 3-D emission
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• Modeling for the various observer’s perspectives:
• Checking the consistency with the local direction of the
Galactic magnetic field
(Leckband et al. 1989, Fulbright & Reynolds 1990, Gaensler 1998)
and, more recently
(Orlando et al. 2007, West et al. 2016, West et al. 2017)
• Latest results: quasi-perpendicular Cosmic-Ray-electrons
acceleration is statistically favoured
BUT STILL UNCLEAR THE CASE OF SN1006
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Smaller-scale magnetic structures
• Mapping with very high resolution
• Analysis of the polarization fraction
(Reynoso et al. 2013 – SN1006)
• Brighter regions show lower polarization fractions. B less ordered there
• Evidence for turbulent B fields where acceleration is more efficient 41
SN 1006: barrel-like or polar caps ?
• Intuitively, a barrel-like 3D structure would
seem more reasonable
• The radial magnetic field the bright limbs,
could either be the sign of a polar cap, or
simply of developed Rayleigh-Taylor like
instabilities
• Rothenflug et al 2004 put forward
quantitatively the argument that, in a
barrel-like structure, the front and back
limb, seen face on, would require a
surface brightness, in the projected
central region, which is not measured
neither in radio nor in non-thermal X-rays
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• That argument is based on the
assumption that synchrotron
emission is isotropic (clearly wrong,
in the presence of polarization)
• For the radio wavelengths range, a
model radial profile has been
computed, which accounts also for
the observed polarization fraction
( / B  1, where  is the magnitude
of the randomly oriented field).
(Bandiera & Petruk 2016)
•  Lower central surface brightness
• Effect even more evident in the Xray, the spectral cutoff.
• Comparison shown in the fully
ordered case

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Conclusions
• Supernova, among others, are a unique laboratory for the study of a
series of problems in plasma physics, wave-particle interaction,
collective effects, etc.
• There are some methods of investigation, like Balmer-line observations,
with a tremendous diagnostic potential.
• Both the quality of observations and the detail of theoretical models have
improved considerably in recent years.
• The only ‘caveat’, is that understanding the geometrical structure of the
system under study may be fundamental to properly match theory and
observations.
Thank you !
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